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Morse Homology for the Yang-Mills Gradient Flow

By Jan Swoboda

Abstract

We use the Yang-Mills gradient flow on the space of connections over a closed Riemann surface to construct a Morse-Bott chain complex. The chain groups are generated by Yang-Mills connections. The boundary operator is defined by counting the elements of appropriately defined moduli spaces of Yang-Mills gradient flow lines that converge asymptotically to Yang-Mills connections.Comment: 83 page

Topics: Mathematics - Differential Geometry, 58E15
Year: 2015
OAI identifier: oai:arXiv.org:1103.0845
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